In the Princeton Companion to Mathematics one reads that even pure mathematicians should know some theoretical physics and applied mathematics. What are some well-organized comprehensive companions to theoretical physics for working mathematicians? I have heard of Armin Wachter and Henning Hoeber's, but I don't know if it is rigorous enough (i.e., for example, there are enough proofs of the theorem given).
[Math] Companion to theoretical physics for working mathematicians
mp.mathematical-physicsphysicsreference-requestsoft-question
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Best Answer
If you allow such a comprehensive reference to re-introduce basic mathematics, then either as a layman or a working mathematician your prayers are answered by the following (he even prefaces by saying that his intended layman-audience must have some mathematical sophistication):
Now let's try to break down the subjects.
Classical Mechanics:
1) Mathematical Methods of Classical Mechanics, by Arnold
2) A Mathematical Introduction to Fluid Mechanics, by Chorin-Marsden
Quantum Mechanics:
1) Mathematical Foundations of Quantum Mechanics, by Mackey
2) The Theory of Groups and Quantum Mechanics, by Weyl
General Relativity:
1) General Relativity for Mathematicians, by Sachs-Wu
2) The Large Scale Structure of Space-Time, by Hawking-Ellis
Electrodynamics:
1) Electromagnetic Theory and Computation: A Topological Approach, by Gross-Kotiuga
2) On the Mathematical Foundations of Electrical Circuit Theory, by Smale
3) This is a plug for Gauge theory:
3a) On Some Recent Developments in Yang-Mills Theory, by Bott
3b) On Some Recent Interactions Between Mathematics and Physics, by Bott
3c) Concept of Nonintegrable Phase Factors and Global Formulation of Gauge Fields, by Wu-Yang
3d) From Superconductors and Four-Manifolds to Weak Interactions, by Witten
Standard Model:
The Algebra of Grand Unified Theories, by Baez-Huerta
Quantum Field Theory and String Theory:
1) Quantum Physics: A Functional Integral Point of View, by Jaffe-Glimm
2) Geometry and Quantum Field Theory, 1994 IAS lectures
3) Quantum Fields and Strings: A Course for Mathematicians, 1996 IAS lectures